The effect of construction material, contents and room geometry on the sound field in dwellings at low frequencies

An experimentally validated finite element method is used to model the sound level in rooms at low frequencies. It is demonstrated that the dimensions of rectangular rooms strongly influence the sound pressure level difference. Additional factors were investigated which are not normally considered in the frequency range where diffuse sound field conditions can be assumed. Three effects were investigated: room damping due to wall vibrations, furniture, the effect of small deviations from simple rectangular shapes. It is confirmed by field measurements that the vibrations of masonry walls and floors introduce less damping than surfaces of lightweight construction. Assigning to the FE model a damping equivalent to a surface absorption of 0.02 reproduces the effect of walls of heavyweight construction. Damping equivalent to a surface absorption of 0.15 reproduces the effects of plastered timber-frame walls, floors and ceilings. The work was briefly extended to a room pair built with heavyweight and lightweight material of construction. The modification of the shape of the room frequency response highlights well the effect of material of construction. In-situ and laboratory measurements show that furniture has little effect on steady-state room response below 100 Hz. Modelling a wall recess smaller than 0.5 m improved the agreement between prediction and measurements but the assumption of a simple rectangular room remains appropriate.     

Applicability of locally reacting boundary conditions to porous material layer backed by rigid wall: Wave-based numerical study in non-diffuse sound field with unevenly distributed sound absorbing surfaces

To clarify the applicability of locally reacting boundary conditions in wave-based numerical analyses of sound fields in rooms, we numerically analyzed a non-diffuse sound field in a room with unevenly distributed sound absorbing surfaces and investigated the differences between the extended and local reactions. Each absorbing surface was a porous material layer backed by a rigid wall. Simulations were performed by the fast multipole boundary element method, a highly efficient boundary element method using the fast multipole method. At low frequencies, the extended and local reactions yielded similar reverberation decay curves because of the influence of the room. However, when the random incidence absorption coefficients were small at low frequencies or frequencies were high, the difference was greater than expected from the corresponding Eyring decay lines. We conclude at high frequencies, the locally reacting boundary conditions lead to a longer reverberation time than that expected from the absorption coefficient differences between the extended and local reactions. These differences were similar in sound-pressure-level and sound-intensity-level distributions, and in the oblique incidence absorption coefficient of the absorbing surfaces, but were increased at low frequencies.     

Theoretical analysis of sound radiation of an elastically supported circular plate

This study focuses on the analysis of the active and reactive sound power of the axisymmetric modes of free vibrations of elastically supported circular plates embedded in a rigid baffle. Some linear and time-harmonic processes have been considered. It is assumed that the plate radiates some acoustic waves into a hemisphere filled with a lossless gaseous medium. The integral formulations for the active and reactive sound power have been derived and expressed in their Hankel representations. They have been used to derive some elementary formulations in the form of some high-frequency asymptotes valid for frequencies higher than the successive coincidence frequencies of the plate. Therefore, the discussion on some sample numerical results mostly covers the sound power radiated at those frequencies. The asymptotes are easy to express in a computer code and they do not need great processor capacity. They are therefore useful for engineering use.The main benefit of the analysis presented in this paper is that the sound power for all the possible boundary configurations of the boundary stiffnesses, i.e., classical clamped, guided, simply supported or completely free boundaries as well as all the intermediate situations, has been described using the same formulae. This is possible simply by changing the two values of stiffnesses associated with the boundary conditions, whose influence on the radiated sound power has been discussed. The solution of the problem of sound power radiated by a vibrating elastically supported circular plate presented herein is essentially more general than the solutions presented earlier for the classical boundary configurations, such as clamped, simply supported, guided or completely free circular plates.     

Low frequency impact sound transmission in dwellings through homogeneous concrete floors and floating floors

An experimentally validated analytical model has been developed in order to investigate the effect on impact sound transmission at low frequencies of location of the impact, type of floor, edge conditions, floor and room dimensions, position of the receiver and room absorption. The model was developed in order to allow rapid repeated calculations necessary for a parametric survey, described in a companion paper. The analytical model uses natural mode analysis to predict the sound field generated in rectangular rooms by point sound sources and the point excitation of homogeneous rectangular plates with different edge conditions. A floor-room model of the sound field generated in a room by a vibrating floor also has been derived. Laboratory and in situ measurements confirm that the models can be used to estimate impact sound transmission at low frequencies. The approach applies to homogeneous simply supported base plates of uniform thickness with homogenous floating floors, which again were experimentally validated in the laboratory and in situ.     

Reduction of acoustic radiation by perforated board and honeycomb layer systems

A perforated system, proposed previously for reducing the radiated sound from a plate at arbitrary frequencies, is applied to three-dimensional problem. Plates are assumed to be supported in a duct of a finite cross-section and excited by a harmonic point force. The sound radiation is investigated from the viewpoint of acoustic power and it is discussed whether the attenuation effect shown previously in the one-dimensional system can be obtained with the three-dimensional system. The effect of support conditions on attenuation characteristics is discussed by using clamped and simply supported circular models. Allowing for the effect, a simply supported rectangular model is studied in detail and its problems are revealed. In order to overcome the problems, a new system including subdivided air cavities in the form of a honeycomb layer instead of a undivided backing cavity is proposed. Each of the honeycomb cells can create local one-dimensional sound fields. Calculated theoretical results are compared to data obtained in a 1/5th scale reverberation chamber. The results for the reduction effect, which are in good agreement, show that the honeycomb layer system can achieve the same reduction of the radiated sound power at arbitrary frequencies as the one-dimensional perforated system.     

四边简支含多孔材料双层板隔声特性

有限大含多孔材料和空气层复合板结构隔声特性的研究尚不充分。该文旨在研究四边简支边界条件下复合板结构隔声特性。首先基于流体饱和多孔弹性介质的声传播理论计算了声波在多孔介质中的传播波数；继而采用四边简支边界条件下板结构的模态函数，利用模态叠加法和伽辽金法推导了复合板结构隔声系数理论模型，并数值求解复合板隔声量。将理论模型得到的四边简支复合板隔声量与实验结果对比，验证了理论模型的正确性。最后，详细讨论了边界条件、板结构尺寸和多孔材料厚度等主要参数对隔声特性的影响。结果表明：四边简支复合结构隔声特性曲线上“谷值”出现得较少，并且简支复合板隔声特性的第一个“吻合频率”比固支支撑复合板更靠近低频，当频率超过3000 Hz以后，简支和固支边界条件复合板结构隔声特性趋于一致。     

Optimization of a clamped plate silencer

A previous theoretical study [L. Huang, J. Acoust. Soc. Am. 119, 2628-2638 (2006)] shows that, in a duct, a simply supported plate covering a side-branch rigid cavity can function effectively as a wave reflector over a broad range of low to medium frequencies. In this study, analytical formulation is extended to the boundary condition of clamped plate, which is easier to implement in practice. The theoretical model is tested experimentally using balsawood, which has a very high stiffness to mass ratio. The spectral peaks and shapes of the measured TL are in agreement with those calculated theoretically, attempts are also made to account for the considerable sound absorption in the rig. Further numerical studies based on the validated model show that, for a uniform plate, the optimal stopband is narrower and the lower band limit is worse than that of the simply supported configuration. However, a wave reflector using nonuniform, clamped plates with thinner ends out-performs the simply supported configuration in every aspect. Analyses show that the improvement is attributed to the increased acoustic radiation efficiency over the bulk length of the nonuniform plate, which behaves more like a rigid plate.     

Using optimized surface modifications to improve low frequency response in a room

A case study of improving sound energy distribution at low frequency in a small orthogonal room is presented in this paper. The effects of the geometric modifications of wall surface on the sound frequency response have been investigated in depth. In order to find the optimal modifications for the wall surface, an optimization procedure, based on finite element analysis, has been developed. The uniqueness of this method is that it takes both modal redistribution and sound diffusion into account during optimization process. As a result, the promising improvements of sound frequency response have been obtained at the frequencies around 100 Hz in all rooms tested, particularly in those where the serious modal concentrations are met. The maximum reduction of sound fluctuation in such a room could reach a mount of 4.6 dB. The work opens up the possibility of improving low frequency sound quality by a means that considers both modal changing and surface scattering at same time.     

Effect of diffusive and nondiffusive surfaces combinations on sound diffusion

One of room acoustic goals, especially in small to medium rooms, is sound diffusion in low frequencies, which have been the subject of lots of researches. Sound diffusion is a very important consideration in acoustics because it minimizes the coherent reflections that cause problems. It also tends to make an enclosed space sound larger than it is. Diffusion is an excellent alternative or complement to sound absorption in acoustic treatment because it doesn’t really remove much energy, which means it can be used to effectively reduce reflections while still leaving an ambient or live sounding space. Distribution of diffusive and nondiffusive surfaces on room walls affect sound diffusion in room, but the amount, combination, and location of these surfaces are still the matter of question. This paper investigates effects of these issues on room acoustic frequency response in different parts of the room with different source-receiver locations. Room acoustic model based on wave method is used (implemented) which is very accurate and convenient for low frequencies in such rooms. Different distributions of acoustic surfaces on room walls have been introduced to the model and room frequency response results are calculated. For the purpose of comparison, some measurements results are presented. Finally for more smooth frequency response in small and medium rooms, some suggestions are made.     

Using optimized wall section to improve low frequency response in a room

Three different wall sections with step shape were applied in the finite element analysis models set up to investigate the effect on low frequency sound field by wall modification. The heights of the step in three cases are taken as equal, random and optimized. The optimized value is obtained by using an optimization process with an objective function of minimum fluctuation in sound field. The frequency responses of rooms with original and modified walls were calculated in a range from 60 Hz to 120 Hz. The results showed that the room with an optimized wall section had the flattest frequency response. Same thing was true as the ratio of the room was changed. The largest improvement on fluctuation reached 4.5 dB. In addition, wall section with semicircle and triangle were studied. The rooms that wall section had optimized radius and heights also gave a better performance than those that had fixed radius and heights. Therefore, it is possible to use optimized wall section to improve low frequency sound field.     

Decay rates and wall absorption at low frequencies

This paper is concerned with evaluating the error of conventional estimates of the boundary absorption of rectangular enclosures, with particular reference to reverberation room sound power measurements. The reverberation process is examined theoretically; the relative contributions to the decay rate from different modes in a rectangular room are calculated from an ensemble average over rooms with nearly the same dimensions. It is shown that the traditional method of determining the absorption of the walls of reverberation rooms systematically underestimates the absorption at low frequencies; the error is computed from the ensemble average. Finally, an unbiased estimate of the sound power radiated by a source in a reverberation room is derived. This estimate involves measurement of the initial decay rates of the room and is, unlike the usual reverberation room sound power estimate, neither based on statistical diffuse field considerations nor on the normal mode theory.     

The effect of different combinations of boundary conditions on the average radiation efficiency of rectangular plates

The boundary conditions of a vibrating plate are known to have an influence on its sound radiation for frequencies below the critical frequency. To investigate this effect in a systematic way, the average radiation efficiency and radiated power are calculated for a rectangular plate set in an infinite baffle using a modal summation approach. Whereas analytical expressions exist for simply supported boundary conditions, a numerical approach is required for other cases. Nine combinations of boundary conditions are considered, consisting of simply supported, clamped and free edges on different plate edges. The structural vibration is approximated by using independent beam functions in orthogonal directions allowing simple approximate formulae for mode shapes and natural frequencies. This assumption is checked against a finite element model and shown to give reliable results. It is shown that a free plate has the lowest radiation efficiency and a clamped plate the highest for most frequencies between the fundamental panel natural frequency and the critical frequency. Other combinations of boundary condition give intermediate results according to the level of constraint introduced. The differences depend on frequency: excluding the extreme case of a fully free plate all the other boundary conditions give results within a range of 8 dB in the middle part of the short-circuiting region, decreasing towards the critical frequency. At low frequency the differences can be even greater, in some cases up to 20 dB. These conclusions are shown to hold for a range of plate thicknesses and dimensions.     

Monotonic curvature of low frequency decay records in reverberation chambers

In the papers by Larsen [1] and Brüel [2], two interesting problems connected with reverberation room measurements are pointed out and discussed. The first problem is that the ensemble averaged decay curve reveals a monotonic curvature at low frequencies. The second phenomenon is that often systematically larger sound power output values are reported at low frequencies according to the free field method than according to the reverberation room method. In searching for an explanation of these anomalies some measurements and a classical normal mode theory analysis have been made. It is shown that it is not possible to explain fully the curvature of the low frequency decay curves by means of the normal mode theory. The measured curves are more bent than the respective theoretical ones. Most probably, it should be possible to explain this lack of agreement by the fact that the absorption characteristics of normal reverberation chambers significantly deviate from the situation of uniform wall admittance which has been assumed in the theoretical deductions. The theoretical analysis and the comparison between theory and practice indicate that the damping characteristics of the individual waves vary much more than is predicted for a uniform wall admittance. This reasoning is supported by the observation that the monotonic curvature increases when a plane concentrated absorbent is added to one of the walls. One way to decrease the curvature has also been identified. When the room surfaces are provided with randomly placed small samples of low frequency absorbents the resulting decay curves turn out to be almost perfectly linear. Furthermore, it is found that the normal mode theory does not imply significantly different sound power output values than the ISO 3741 model. This fact has been verified with a comparative test. According to the normal mode theory the average sound power output as measured in the reverberant room should equal the free field output. Therefore, one is forced to conclude that the analysis of the classical normal mode theory fails in explaining the anomalies observed.     

住宅建筑中相邻房间的侧向传声预测

侧向传声作为建筑中声传递的组成部分,对住宅的整体隔声效果具有重要的影响,通过将建筑中相邻房间的各建筑构件划分为若干子系统,应用统计能量分析(Statistical Energy Analysis,SEA)理论,从系统的声功率平衡的角度建立侧向传声的预测模型,在描述各路径的传声规律的同时确定主要传声路径。研究结果表明:当外围护结构为重质结构,且为匀质单一材料构造时,(1)在低频处,全程通过两相邻房间的侧墙或楼板的非通过隔墙的侧向路径成为主要侧向传声路径;(2)在中高频,各侧向路径的声压级差趋于一致,此时的建筑隔声性能取决于通过隔墙的直接路径上的声传递;(3)采用重质隔墙可以缩小侧向传声影响的频率范围。本研究为改善住宅的声环境质量及建筑隔声设计提供了理论依据。      

A hybrid finite element – statistical energy analysis approach to robust sound transmission modeling

When considering the sound transmission through a wall in between two rooms, in an important part of the audio frequency range, the local response of the rooms is highly sensitive to uncertainty in spatial variations in geometry, material properties and boundary conditions, which have a wave scattering effect, while the local response of the wall is rather insensitive to such uncertainty. For this mid-frequency range, a computationally efficient modeling strategy is adopted that accounts for this uncertainty. The partitioning wall is modeled deterministically, e.g. with finite elements. The rooms are modeled in a very efficient, nonparametric stochastic way, as in statistical energy analysis. All components are coupled by means of a rigorous power balance. This hybrid strategy is extended so that the mean and variance of the sound transmission loss can be computed as well as the transition frequency that loosely marks the boundary between low- and high-frequency behavior of a vibro-acoustic component. The method is first validated in a simulation study, and then applied for predicting the airborne sound insulation of a series of partition walls of increasing complexity: a thin plastic plate, a wall consisting of gypsum blocks, a thicker masonry wall and a double glazing. It is found that the uncertainty caused by random scattering is important except at very high frequencies, where the modal overlap of the rooms is very high. The results are compared with laboratory measurements, and both are found to agree within the prediction uncertainty in the considered frequency range.     

Spatially extended sound equalization in rectangular rooms.

The results of a theoretical study on global sound equalization in rectangular rooms at low frequencies are presented. The zone where sound equalization can be obtained is a continuous three-dimensional region that occupies almost the complete volume of the room. It is proved that the equalization of broadband signals can be achieved by the simulation of a traveling plane wave using FIR filters. The optimal solution has been calculated following the traditional least-squares approximation, where a modeling delay has been applied to minimize reverberation. An advantage of the method is that the sound field can be estimated with sensors placed in the limits of the equalization zone. As a consequence, a free space for the listeners can be obtained.     

Modeling the sound transmission between rooms coupled through partition walls by using a diffusion model

In this paper, a modification of the diffusion model for room acoustics is proposed to account for sound transmission between two rooms, a source room and an adjacent room, which are coupled through a partition wall. A system of two diffusion equations, one for each room, together with a set of two boundary conditions, one for the partition wall and one for the other walls of a room, is obtained and numerically solved. The modified diffusion model is validated by numerical comparisons with the statistical theory for several coupled-room configurations by varying the coupling area surface, the absorption coefficient of each room, and the volume of the adjacent room. An experimental comparison is also carried out for two coupled classrooms. The modified diffusion model results agree very well with both the statistical theory and the experimental data. The diffusion model can then be used as an alternative to the statistical theory, especially when the statistical theory is not applicable, that is, when the reverberant sound field is not diffuse. Moreover, the diffusion model allows the prediction of the spatial distribution of sound energy within each coupled room, while the statistical theory gives only one sound level for each room.     

Mechanism and calculation of the niche effect in airborne sound transmission

The goal is to interpret and calculate the "niche effect" for the airborne sound transmission through a specimen mounted inside an aperture in the wall between the source and receiving reverberation rooms. The low-frequency sound insulation is known to be worse for the specimen placed at the center than for the specimen mounted at either edge of the aperture. As shown, the aperture with a tested specimen can be simulated at low frequencies as a triple partition where the middle element is the specimen and the role of the edge leaves is played by the air masses entrained at the aperture edges. With a centrally located specimen, such a triple system is symmetric and has two main natural frequencies close together. In this case, the resonant transmission is higher than for the edge arrangement simulated as a double system with one natural frequency. Analogous resonant phenomena are known to reduce the low-frequency transmission loss for symmetric triple windows or solid walls with identical air gaps and lightweight boards on both sides. The theoretical results obtained for the mechanical and acoustical models are in a good agreement with the experimental data.     

Prediction of sound flanking transmission through two adjacent rooms within a residence building

Flanking transmission has significant effects on the overall sound insulation of two adjacent rooms within a residence building. This study investigates the mechanism of the sound flanking transmission by dividing it into several subsystems with the statistical energy analysis method. The sound energy equations of these subsystems are obtained first, and then,the sound transmissions on each flanking path are predicted and the dominant sound transmission path is determined by solving these equations and calculating the total loss factors of the subsystems and coupling loss factors between subsystems. With respect to a masonry building with heavy-weight homogeneous structure, the results show that:(1) the flanking transmission paths instead of the separating wall may become the dominant ones at low frequencies;(2) all sound transmissions on the flanking paths tend to be consistent at medium and high frequencies, so the sound insulation between two adjacent rooms depends on the direct path of the separating wall;(3) heavy-weight separating walls can be used to reduce the frequency range of the flanking transmission.     

钢结构装配式住宅墙板连接方式对隔声性能的影响*

为提升其隔声性能,通过有限元法数值分析,比较了不同位置墙板的连接方式对房间隔声性能的影响。结果表明：(1)侧墙墙板柔性连接处理对侧向传声的抑制作用显著,当侧墙墙板采用柔性连接后,房间的隔声量在低频段平均可以提升3 dB左右;(2)公共隔墙墙板的柔性连接对房间低频段隔声量提升不明显,甚至在160 Hz、400 Hz、500 Hz等频率下隔声量有所降低。最后,基于模拟分析结果对装配式墙体连接方式提出了改进策略。